Explore fractional Gaussian and stable random fields on fractals in this conference talk by Céline Lacaux. Delve into the mathematical concepts of Gaussian fields, covariance functions, and stochastic integrals. Examine key properties, including the Laplace operator and square integrability. Learn about the semigroup PT and the work of Baru and Perkins. Understand the definition and sample applications of these complex mathematical structures. Recorded during the thematic meeting "Multifractal analysis and self-similarity" at the Centre International de Rencontres Mathématiques in Marseille, France, this 58-minute presentation offers valuable insights for mathematicians and researchers in related fields.